Creating a UV Map from a shrinkwrapped sphere
Spherical projection

The above is the equirectangular projection of the Tissot Index Plate Carrie projection image found here Justin Kunimune / CC BY-SA (https://creativecommons.org/licenses/by-sa/4.0)  onto a squashed 8 sided ngon filled cylinder.

The node set up explained in this answer https://blender.stackexchange.com/a/159492/15543
A Hammer Projection
and again using a Hammer Projection node setup as explained here of
Tissot index hammer projection image from wiki by Justin Kunimune CC BY-SA 4.0